Abstract We bound the number of distinct minimal subsystems a given transitive subshift linear complexity, continuing work Ormes and Pavlov [On complexity function for sequences which are not uniformly recurrent. Dynamical Systems Random Processes (Contemporary Mathematics, 736) . American Mathematical Society, Providence, RI, 2019, pp. 125--137]. also generic measures such can support based on...

In this paper, we investigate team optimal control of coupled major-minor subsystems with mean-field sharing. In such a model, there is one major subsystem that directly influences the dynamics of n homogeneous minor subsystems; however, the minor subsystems influence the dynamics of the major subsystem and each other only through their mean behaviour (indirectly). In this model, the major and ...

The notion of entanglement quantum states is usually defined with respect to a fixed bipartition. Indeed, global basis change can always map an entangled state separable one. situation however different when considering set states. In this work we define the "absolutely set" states: for any possible choice basis, at least one in entangled. Hence, all bipartitions, i.e. definition subsystems, fe...

Let X,Y be finite sets, r,s,h,??N with s?r,X?Y. By ?Xh we mean the collection of all h-subsets X where each subset occurs ? times. A coloring (partition) is r-regular if element in exactly r subsets color. one-regular color class a perfect matching. We are interested necessary and sufficient conditions under which an can embedded into s-regular ?Yh. Using algebraic techniques involving glueing ...